Local Form
Each quadratic differential on a domain in the complex plane may be written as where is the complex variable and is a complex valued function on . Such a `local' quadratic differential is holomorphic if and only if is holomorphic. Given a chart for a general Riemann surface and a quadratic differential on, the pull-back defines a quadratic differential on a domain in the complex plane.
Read more about this topic: Quadratic Differential
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